We follow very closely Föllmer and Kabanov Lagrange multiplier approach to superstrategies in perfect incomplete markets, except that we provide a very simple proof of the existence of a minimizing multiplier in case of a European option under the assumption that the discounted process of the underlying is an $L^2\left( P\right) $ martingale for some probability $P.$ Even if it gives the existence of a superstrategy associated to the supremum of the expectations under the equivalent martingale measures, our result is much weaker than the optional decomposition theorem.